Why the raw quotes need smoothing
Raw, option-by-option implied volatility is noisy. Bid/ask spread, stale quotes, and thin strikes each inject error into a single reading — two option contracts a dollar apart in strike can show implied volatilities that don't belong on the same smooth curve.
Surface modeling fits a smooth, arbitrage-free curve through the noisy points instead, so that every downstream metric — skew, term structure, the volatility risk premium — measures the underlying signal rather than quote noise.
SVI and the variance surface
SVI, Stochastic Volatility Inspired, is an industry-standard parametric model — five parameters per expiration — that fits a smooth curve to implied variance across strikes. It is widely used because it calibrates quickly and, with the right parameter constraints, can be made arbitrage-free. It is the model behind every "smoothed" implied volatility figure used elsewhere in this library.
The variance surface is the full grid of SVI-fitted variance across every strike and expiration at once — the single three-dimensional object that skew, term structure, and the smile are each just a two-dimensional slice of. Arbitrage Flags run two automated checks against it: butterfly arbitrage, where the smile curves so sharply it implies a negative probability somewhere, and calendar arbitrage, where variance decreases as expiry lengthens when it should not. A flagged surface means the raw quotes feeding it are internally inconsistent, and any derived metric built from it should be treated cautiously until it clears.
What comes out of the fit
A variance swap prices fair variance from the entire strike curve rather than just the at-the-money quote; Fair Vol is its square root — a more robust reference point than a single raw at-the-money reading, especially when the smile is skewed or thin. SVI-Smoothed IV is simply the de-noised implied volatility read directly off the fitted curve at any strike — the number most of the site's downstream metrics actually consume.
Convexity Premium is wing implied volatility minus at-the-money implied volatility on the smoothed curve — a rising premium means the market is paying up for tail protection relative to the middle of the distribution. Smile Ratio, the ratio of twenty-five-delta put volatility to twenty-five-delta call volatility, is a cleaner, standardized version of skew: above one is the typical put-rich shape, at or below one flags a name where call demand is catching up or overtaking. Tail Convexity reads how sharply the deep out-of-the-money put wing curves relative to the rest of the smile — a specific read on crash pricing, distinct from the more general downside skew.